Discrete Mathematics Mock Test 1

10%

Question 1 of 10

1. Which of the arguments is not valid in proving sum of two odd number is not odd.

2n +1 + 2m +1 = 2(n+m+1) hence true for all

All of the mentioned

None of the mentioned

3 + 3 = 6, hence true for all

Question 1 of 10

Question 2 of 10

2. ~ A v ~ B is logically equivalent to?

B V A

~ A ∧ ~ B

~ A → ~ B

A → ~B

Question 2 of 10

Question 3 of 10

3. The converse of p → q is the proposition of _______________

¬q → ¬p

¬q → p

q → p

¬p → ¬q

Question 3 of 10

Question 4 of 10

4. The statement which is logically equivalent to A∧ (and) B is?

~A ∧ ~ B

~(A->~B)

A ∧ ~B

A->B

Question 4 of 10

Question 5 of 10

5. What are the converse of the conditional statement “When Raj stay up late, it is necessary that Raj sleep until noon.”

“If Raj stay up late, then Raj sleep until noon.”

“If Raj sleep until noon, then Raj stay up late.”

“If Raj does not stay up late, then Raj does not sleep until noon.”

“If Raj does not sleep until noon, then Raj does not stay up late.”

Question 5 of 10

Question 6 of 10

6. Let P: We give a nice overall squad performance, Q: We will win the match.
Then the symbolic form of “We will win the match if and only if we give a nice overall squad performance.“ is?

Q<->P

~P v Q

P v Q

Q ∧ P

Question 6 of 10

Question 7 of 10

7. The statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.

∀x(C(x) ∧ F (x))

∃x(C(x) → F (x))

∀x(C(x) → F (x))

∃x(C(x) ∧ F (x))

Question 7 of 10

Question 8 of 10

8. Find a counterexample of ∀x∀y(xy > y), where the domain for all variables consists of all integers.

x = -1, y = 17

x = -2 y = 8

Does not have any counter example

Both x = -1, y = 17 and x = -2 y = 8

Question 8 of 10

Question 9 of 10

9. If in a bits string of {0,1}, of length 4, such that no two ones are together. Then the total number of such possible strings are?

Question 9 of 10

Question 10 of 10

10. (A ∨ F) ∨ (A ∨ T) is always _________

True

False

Question 10 of 10